 | Aaron Schuyler - Navigation - 1873 - 536 pages
...A»a. 1.03068. DIVISION BY LOGAEITHMS. 16. Proposition. The logarithm of the quotient of two KMM&CTT it equal to the logarithm of the dividend minus the logarithm of the divisor. • (1) 6•= TO; then, bv del. log » = z. Let ' I (2) 6 • = n; then, by de£. log n = y. = "; then,byde£,... | |
 | Aaron Schuyler - Measurement - 1875 - 284 pages
...75831.667. 5. Find the product of 85, .097, and .125. Ans. 1.03062. DIVISION BY LOGARITHMS. 16. Proposition. The logarithm of the quotient of two numbers is equal...of the dividend minus the logarithm of the divisor. Г (1) b" = m; then, by def., log m = x. Let i. (_ (2) b * — - n; then, by def., log n — у. (1)... | |
 | Carl Bremiker - Logarithms - 1875 - 544 pages
...two factors taken separately. Further, the logarithm of the quotient of one number divided by another is equal to the logarithm of the dividend minus the logarithm of the divisor. The logarithm of the power of any quantity is equal to the product of the logarithm of the quantity... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...those numbers. Also, since powers of the same quantity are divided by subtracting their exponents, the logarithm of the quotient of two numbers is equal to the logarithm of the dividend diminished by that of the divisor. Since the logarithm of 10 is 1, if a number be multiplied or divided.by... | |
 | Benjamin Greenleaf - Algebra - 1879 - 376 pages
...member by member, We have, in which in which, x -\- y = loga m n. 359. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. For, assume the equations, ax = m, a" = n, and dividing, member by member, we have , „ in ax~>> —... | |
 | Benjamin Greenleaf - 1879 - 346 pages
...equations, member by member, We have, in which, x 4- y = Ioga m n. 359. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. For, assume the equations, a* = wi, ai — n, and dividing, member by member, we have in which x —... | |
 | R. M. Milburn - Mathematics - 1880 - 116 pages
...product is equal to the sum of the logarithms of its factors. 103. or, the logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. 104. loga m"=n loga m; n being integral or fractional. _ i j. 105. loga ?/m=loga m* = - loga m, n 106.... | |
 | George Albert Wentworth - Algebra - 1881 - 400 pages
...like manner, the proposition may be extended to any number of factors. II. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. For, let m and n be two numbers, and x and y their logarithms. Then m = of, and n = a?. Hence, m +... | |
 | Henry Law - 1884 - 568 pages
...or, the sum of the logarithms of m and n is the logarithm of their product. PROPOSITION N. THEOREM. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend, with the logarithm of the divisor subtracted from it. Let X and I denote the same as in the foregoing... | |
 | Edward Brooks - Algebra - 1888 - 344 pages
...log (MxN). Or, log ( M x Л) - log M+ log N. PRIN. 4. The logarithm of the quotient of two numbers ù equal to the logarithm of the dividend minus the logarithm of the divisor. For, let m = log M, and n = log N. Then, B" = M, B*=N. Dividing, S^~jn = MiN. Hence, log ( M •*•... | |
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The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log 
